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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some Diophantine equations of the form $x^{2}-py^{2} =z$


Author: Walter Feit
Journal: Proc. Amer. Math. Soc. 129 (2001), 623-625
MSC (2000): Primary 11D09, 11R11
Published electronically: October 2, 2000
MathSciNet review: 1800243
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $p = a^{2} + (2b)^{2}$ be a prime. It is shown that each of the two Diophantine equations $x^{2}-py^{2} =a$ or $4b$ has integral solutions.


References [Enhancements On Off] (What's this?)

  • [G] Carl Friedrich Gauss, Disquisitiones arithmeticae, Translated into English by Arthur A. Clarke, S. J, Yale University Press, New Haven, Conn.-London, 1966. MR 0197380 (33 #5545)
  • [L] A.-M. Legendre, Théorie des nombres, Librairie Scientifique et Technique, A. Blanchard, Paris, 1955.

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Additional Information

Walter Feit
Affiliation: Department of Mathematics, Yale University, Box 208283, New Haven, Connecticut 06520-8283
Email: feit@math.yale.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-06025-1
PII: S 0002-9939(00)06025-1
Keywords: Quadratic field, prime
Received by editor(s): January 20, 2000
Published electronically: October 2, 2000
Communicated by: David Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society